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Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells

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  • Shuo Liu
  • Lina Ma
  • Jianquan Li
  • Qingbo Zhao

Abstract

By introducing the probability function describing latency of infected cells, we unify some models of viral infection with latent stage. For the case that the probability function is a step function, which implies that the latency period of the infected cells is constant, the corresponding model is a delay differential system. The model with delay of latency and two types of target cells is investigated, and the obtained results show that when the basic reproduction number is less than or equal to unity, the infection‐free equilibrium is globally stable, that is, the in‐host free virus will be cleared out finally; when the basic reproduction number is greater than unity, the infection equilibrium is globally stable, that is, the viral infection will be chronic and persist in‐host. And by comparing the basic reproduction numbers of ordinary differential system and the associated delayed differential system, we think that it is necessary to elect an appropriate type of probability function for predicting the final outcome of viral infection in‐host.

Suggested Citation

  • Shuo Liu & Lina Ma & Jianquan Li & Qingbo Zhao, 2013. "Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:632381
    DOI: 10.1155/2013/632381
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    1. Alan S. Perelson & Paulina Essunger & Yunzhen Cao & Mika Vesanen & Arlene Hurley & Kalle Saksela & Martin Markowitz & David D. Ho, 1997. "Decay characteristics of HIV-1-infected compartments during combination therapy," Nature, Nature, vol. 387(6629), pages 188-191, May.
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    Cited by:

    1. Sara Bidah & Omar Zakary & Mostafa Rachik & Hanane Ferjouchia, 2020. "Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree‐Disagree Opinion Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).

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